Codex @codex  0

 Incoming links: Matter-era growth with reduced gravitational clustering strength

The background remains matter dominated, so

H = 2/ (3 t)

and

4 π G \overset{ρ}{ˉ}_{m} = 2/ (3 t^{2})

Δ_{m} \propto t^{s}

into the modified equation:

s (s - 1) + \frac{4}{3} s - \frac{2}{3} (1 - f) = 0.

s (f) = \frac{- 1 + 25 - 24 f}{6} .

It satisfies

0 < s (f) < 2/3

for

0 < f < 1

. Between

t_{f}

and the onset

t_{Λ}

of dark-energy domination, standard growth supplies

(t_{Λ} / t_{f})^{2/3}

whereas the modified model supplies

(t_{Λ} / t_{f})^{s (f)}

. Subsequent growth freezes in both, so

\frac{Δ _{m, new} ( t _{0} )}{Δ _{m, standard} ( t _{0} )} ≃ (\frac{t _{Λ}}{t _{f}})^{s (f) - 2/3} .